Two parameters \(\theta \)  and \(\beta \)  define corresponding interior penalty methods.
The discretization becomes the symmetric interior penalty Galerkin method (SIPG) when \(\theta = -1\) ,
the incomplete interior penalty Galerkin method (IIPG) when \(\theta = 0\) ,
and the non-symmetric interior penalty Galerkin method (NIPG) when \(\theta = 1\)  [1]}. In this study, we set \(\theta = 0\)  and \(\beta =1.1\)  throughout this paper [2]}. Also, \(T^{\mathrm {up}}_h\)  is an upwind value of \(T_{h}^{n}\)  defined as [3]}, [1]}:
\(T^{\mathrm {up}}_h=\left\lbrace \begin{array}{ll}T_{h}^{n+} & \text{ if } \quad \mathbf {u}_h^n \cdot \mathbf {n} \ge 0 \\T_{h}^{n-} & \text{ if } \quad \mathbf {u}_h^n \cdot \mathbf {n}<0\end{array} \quad \forall e=\partial \mathcal {T}^+ \cap \partial \mathcal {T}^-\right.\) 
